POPL '81 Proceedings of the 8th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Universal schemes for parallel communication
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Efficient schemes for parallel communication
PODC '82 Proceedings of the first ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Constructing a perfect matching is in random NC
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Parallel graph algorithms that are efficient on average
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
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A perfect matching in a graph G(V,E), also called a 1-factor, is a collection P of non-interesting edges engaging (incident with) all the vertices; in case G is bipartite V &equil; M @@@@ F, M @@@@ F &equil; &fgr;, P should engage all the vertices of M. The combinatorial problem of finding a perfect matching in G (and its rich ramifications) were extensively studied (and applied) from existential, algorithmic and probabilistic points of view. Here we replace sequential algorithms by distributive, parallel ones. We imagine N processors without a shared memory or a central coordinator (except a clock) reside at the N vertices and communicate by messages. For each particular problem, the edges (giving direct connections) are given and define the input graph G. The collectin of all these graphs is made into a probability space GN (in several ways, as explicated below). In one synchronized Step (&equil; beat), each processor can send a message to a neighbor along an edge of G. One can cheaply implement such steps, uniformly for all graphs, with an efficient switchboard.